1. Field of the Invention
The present invention relates to a method for estimating phase error in MIMO OFDM communications system, and more particularly, to a method for estimating phase error existing in the receiver of the MIMO OFDM communications system.
2. Description of the Prior Art
Please refer to FIG. 1. FIG. 1 is a diagram illustrating a conventional Multiple Input Multiple Output (MIMO) Orthogonal Frequency Division Multiplexing (OFDM) communications system 100. It is noted that the MIMO OFDM communication system here includes Multiple Input Single Output (MISO) OFDM communication system, for example, a 2T1 R OFDM system, i.e. the number of the transmitting antennas TX is 2, and the number of the receiving antennas RX is 1.
The MIMO OFDM communications system 100 comprises a transmitter 110 for transmitting radio frequency signals and a receiver 120 for receiving radio frequency signals from the transmitter 110.
The transmitter 110 comprises a modulation device 111, a space-time-frequency processing device 112, a transmitting signal transforming module 116, and a plurality of transmitting antennas TX.
The transmitting signal transforming module 116 comprises an Inverse Fast Fourier Transform (IFFT) device 113, a Digital/Analog Converter (DAC) 114, and an RF (radio frequency) circuit 115.
The modulation device 111 is disposed for modulating data. The space-time-frequency processing device 112 is coupled to the modulation device 111 and disposed for processing the modulated data. The transmitting signal transforming module 116 is coupled between the space-time-frequency processing device 112 and the transmitting antennas TX for receiving the processed data from the space-time-frequency processing device 112 and transforming the received data to radio frequency signals to the transmitting antennas TX. More particularly, in the transmitting signal transforming module 116, the IFFT device 113 is coupled to the space-time-frequency processing device 112 and disposed for executing IFFT on the processed modulated data and accordingly outputting transformed data; the DAC 114 is coupled to the IFFT device 113 and disposed for converting the transformed data to analog signals; the RF circuit 115, coupled to the DAC 114, receives the analog signals and accordingly up-converts the received analog signals to radio frequency signals. The antennas TX, coupled to the RF circuit 115 of the transmitting signal transforming module 116, receives the radio frequency signals from the RF circuit 115 and transmits the received radio frequency signals.
The receiver 120 comprises a plurality of receiving antennas RX, a receiving signal transforming module 130, a timing/phase compensation device 123, an equalizer 124, a demodulation device 125, and a Phase Lock Loop (PLL) 126.
The receiving signal transforming module 130 comprises an RF circuit 127, an Analog/Digital Converter (ADC) 121, and an FFT device 122.
The receiving antennas RX receive the radio frequency signals transmitted from the transmitting antennas TX of the transmitter 110. The receiving signal transforming module 130 is coupled between the receiving antennas RX for receiving the radio frequency signals and transforming the received radio frequency signals to transformed signals to the time/phase compensation device 123. More particularly, in the receiving signal transforming module 130, the RF circuit 127, coupled to the receiving antennas RX, down-converts the radio frequency signals received from the receiving antennas RX, i.e., a plurality of receiving paths, to base band or intermediate band analog signals; the ADC 121, coupled to the RF circuit 127, converts the analog signals from the RF circuit 127 to digital signals; the FFT device 122, coupled to the ADC 121, executes FFT on the digital signals received from the ADC 121 and accordingly outputs transformed signals. The timing/phase compensation device 123, coupled to the FFT device 122 of the receiving signal transforming module 130, compensates the transformed signals according to the phase outputted from the PLL 126. The equalizer 124, coupled to the timing/phase compensation device 123, the demodulation device 125, and the PLL 126, equalizes the compensated signals from the timing/phase compensation device 123 and accordingly outputs to the demodulation device 125, and estimates phase error θ of the received compensated signals and outputs the estimated phase error θ to the PLL 126. The PLL 126, coupled to the equalizer 124, receives the phase error θ and accordingly adjusts its phase, and outputs a clock signal with the adjusted phase to the timing/phase compensation device 123. The demodulation device 125, coupled to the equalizer 124, demodulates the equalized signals and accordingly outputs data.
Because of frequency mismatch, timing drift or Common Phase Error (CPE), a phase error θ exists between the actual received signal and the correct signal. Therefore, in data tones, the equalizer 124 is utilized to estimate the phase error θ of the received signal and accordingly outputs the estimated phase error θ to the PLL 126 since the data signal can be extracted from the received radio frequency signal. Consequently, the PLL 126 enables the timing/phase compensation device 123 to correctly compensate the timing/phase of the received signals. The equalizer 124 can be a zero-forcing (ZF) equalizer.
Assuming the number of the transmitting antennas TX is 2, and the number of the receiving antennas RX is 3 (a 2T3R OFDM communications system), therefore, the received signals (after being fast Fourier transformed) can be derived from the following equations:
                                          [                                          y                                  1                  ,                  t                                            ⁢                                                          ⁢                              y                                  1                  ,                                      t                    +                    1                                                                        ]                    =                                                    [                                                      h                    11                                    ⁢                                                                          ⁢                                      h                    12                                                  ]                            ⁡                              [                                                                                                                              x                          1                                                ⁢                                                  ⅇ                          jθ                                                                                                                                                              x                          2                                                ⁢                                                  ⅇ                          jθ                                                                                                                                                                                                  -                                                      x                            2                            *                                                                          ⁢                                                  ⅇ                          jθ                                                                                                                                                              x                          1                          *                                                ⁢                                                  ⅇ                          jθ                                                                                                                    ]                                      +                          [                                                n                                      1                    ,                    t                                                  ⁢                                                                  ⁢                                  n                                      1                    ,                                          t                      +                      1                                                                                  ]                                      ;                            (        1        )                                                      [                                          y                                  2                  ,                  t                                            ⁢                                                          ⁢                              y                                  2                  ,                                      t                    +                    1                                                                        ]                    =                                                    [                                                      h                    21                                    ⁢                                                                          ⁢                                      h                    22                                                  ]                            ⁡                              [                                                                                                                              x                          1                                                ⁢                                                  ⅇ                          jθ                                                                                                                                                              x                          2                                                ⁢                                                  ⅇ                          jθ                                                                                                                                                                                                  -                                                      x                            2                            *                                                                          ⁢                                                  ⅇ                          jθ                                                                                                                                                              x                          1                          *                                                ⁢                                                  ⅇ                          jθ                                                                                                                    ]                                      +                          [                                                n                                      2                    ,                    t                                                  ⁢                                                                  ⁢                                  n                                      2                    ,                                          t                      +                      1                                                                                  ]                                      ;                            (        2        )                                                      [                                          y                                  3                  ,                  t                                            ⁢                                                          ⁢                              y                                  3                  ,                                      t                    +                    1                                                                        ]                    =                                                    [                                                      h                    31                                    ⁢                                                                          ⁢                                      h                    32                                                  ]                            ⁡                              [                                                                                                                              x                          1                                                ⁢                                                  ⅇ                          jθ                                                                                                                                                              x                          2                                                ⁢                                                  ⅇ                          jθ                                                                                                                                                                                                  -                                                      x                            2                            *                                                                          ⁢                                                  ⅇ                          jθ                                                                                                                                                              x                          1                          *                                                ⁢                                                  ⅇ                          jθ                                                                                                                    ]                                      +                          [                                                n                                      3                    ,                    t                                                  ⁢                                                                  ⁢                                  n                                      3                    ,                                          t                      +                      1                                                                                  ]                                      ;                            (        3        )                                                      Y                          6              ×              1                                =                                                    [                                                                                                    y                                                  1                          ,                          t                                                                                                                                                                        y                                                  1                          ,                                                      t                            +                            1                                                                          *                                                                                                                                                y                                                  2                          ,                          t                                                                                                                                                                        y                                                  2                          ,                                                      t                            +                            1                                                                          *                                                                                                                                                y                                                  3                          ,                          t                                                                                                                                                                        y                                                  3                          ,                                                      t                            +                            1                                                                          *                                                                                            ]                                            6                ×                1                                      =                                                                                H                                          6                      ×                      2                                                        ·                                      X                                          2                      ×                      1                                                                      +                                  N                                      6                    ×                    1                                                              =                                                                                                                  [                                                                                                                                            h                                11                                                                                                                                                    -                                                                  h                                  12                                                                                                                                                                                                                                        h                                12                                *                                                                                                                                                    +                                                                  h                                  11                                  *                                                                                                                                                                                                                                        h                                21                                                                                                                                                    -                                                                  h                                  22                                                                                                                                                                                                                                        h                                22                                *                                                                                                                                                    +                                                                  h                                  21                                  *                                                                                                                                                                                                                                        h                                31                                                                                                                                                    -                                                                  h                                  32                                                                                                                                                                                                                                        h                                32                                *                                                                                                                                                    +                                                                  h                                  31                                  *                                                                                                                                                                    ]                                                                    6                        ×                        2                                                              ⁡                                          [                                                                                                                                                                  x                                1                                                            ⁢                                                              ⅇ                                jθ                                                                                                                                                                                                                                                        x                                2                                *                                                            ⁢                                                              ⅇ                                jθ                                                                                                                                                        ]                                                                            2                    ×                    1                                                  +                                                      [                                                                                                                        n                                                          1                              ,                              t                                                                                                                                                                                                        n                                                          1                              ,                                                              t                                +                                1                                                                                      *                                                                                                                                                                            n                                                          2                              ,                              t                                                                                                                                                                                                        n                                                          2                              ,                                                              t                                +                                1                                                                                      *                                                                                                                                                                            n                                                          3                              ,                              t                                                                                                                                                                                                        n                                                          3                              ,                                                              t                                +                                1                                                                                      *                                                                                                                ]                                                        6                    ×                    1                                                                                      ;                            (        4        )                                                                                    G                                  2                  ×                  6                                            =                            ⁢                                                pinv                  ⁡                                      (                    H                    )                                                  =                                                                            (                                                                        H                                                      6                            ×                            2                                                    H                                                ·                                                  H                                                      6                            ×                            2                                                                                              )                                                              -                      1                                                        ·                                      H                                          6                      ×                      2                                        H                                                                                                                                          =                                ⁢                                                      1                                                                  ∑                                                  i                          =                                                      1                            :                            3                                                                                              ⁢                                                                                          ⁢                                                                        ∑                                                      j                            =                                                          1                              :                              2                                                                                                      ⁢                                                                                                  ⁢                                                  h                          ij                          2                                                                                                      ·                                      [                                                                                                                        +                                                          h                              11                              *                                                                                                                                                            +                                                          h                              12                                                                                                                                                            +                                                          h                              21                              *                                                                                                                                                            +                                                          h                              22                                                                                                                                                            +                                                          h                              31                              *                                                                                                                                                            +                                                          h                              32                                                                                                                                                                                                        -                                                          h                              12                              *                                                                                                                                                            +                                                          h                              11                                                                                                                                                            -                                                          h                              22                              *                                                                                                                                                            +                                                          h                              21                                                                                                                                                            -                                                          h                              32                              *                                                                                                                                                            +                                                          h                              31                                                                                                                                            ]                                                              ;                                                          (        5        )                                                      X                          2              ×              1                                =                                    [                                                                                                                  x                        1                                            ⁢                                              ⅇ                        jθ                                                                                                                                                                                x                        2                        *                                            ⁢                                              ⅇ                        jθ                                                                                                        ]                        =                                                            G                                      2                    ×                    6                                                  ·                                  Y                                      6                    ×                    1                                                              +                              N                                  2                  ×                  1                                                                    ;                            (        6        )            
where * represents the complex conjugate of the corresponding symbol (each symbol in the equations (1)˜(6) are complex numbers), X2×1 represents the data signal matrix, Y6×1 represents the received signal matrix after being fast Fourier transformed, H represents the channel coefficient matrix, G2×6 represents the gain matrix, N2×1 represents the noise matrix, HH represents the Hermitian transpose of the channel coefficient matrix H, each element hij in the matrix H represents the channel coefficient between one transmitting antenna and one receiving antenna, nj and nj,t+1 represent noise, yi,t and yi,t+1 represents the received signals from the Ith receiving antennas RX after being fast Fourier transformed, and xj represents the data signal. Therefore, in data tone, the equalizer 124 can estimate the phase error θ according to the equations (1)˜(6). The PLL 126 adjusts its phase according to the estimated phase error θ and enables the timing/phase compensation device 123 to correctly compensate the timing/phase of the received signals.
However, in the equation (6), the value of the gain of the gain matrix G is not relatively large enough (compared to the noise), and thus the noise matrix N cannot be ignored, which affects the accuracy of the estimation of the phase error θ.
Furthermore, in the MIMO OFDM communications system, the number of the receiving antennas has to be larger than the number of the transmitting antennas. In other words, the number of the receiving antennas cannot be less than the number of the transmitting antennas. Assuming the number of the transmitting antennas TX is 2, and the number of the receiving antennas RX is 1 (a 2T1R OFDM communications system), therefore, the received signals can be derived from the following equations:
                                          y            1                    =                                                    [                                                      h                    11                                    ⁢                                                                          ⁢                                      h                    12                                                  ]                            ⁡                              [                                                                                                                              x                          1                                                ⁢                                                  ⅇ                          jθ                                                                                                                                                                                                  x                          2                                                ⁢                                                  ⅇ                          jθ                                                                                                                    ]                                      =                                                            (                                                                                    h                        11                                            ⁢                                              x                        1                                                              +                                                                  h                        12                                            ⁢                                              x                        2                                                                              )                                ⁢                                  ⅇ                  jθ                                            +              noise                                      ;                            (        7        )            where y1 represents the received signal after being fast Fourier transformed, x1 and x2 represent the pilot signals, h11 and h12 represent the channel coefficients. If x1=1, x2=−1, and h11, and h12 are almost the same, in this condition, the received signal y1 approximately equals the noise, and consequently the phase error θ cannot be estimated, which is why in the MIMO OFDM communications system, the number of the receiving antennas has to be larger than the number of the transmitting antennas.